On the Discretization of Truncated Integro-Differential Sweeping Process and Optimal Control

Abderrahim Bouach, Tahar Haddad and Lionel Thibault ()
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Abderrahim Bouach: Université Mohammed Seddik Benyahia, Jijel
Tahar Haddad: Université Mohammed Seddik Benyahia, Jijel
Lionel Thibault: Université de Montpellier

Journal of Optimization Theory and Applications, 2022, vol. 193, issue 1, No 33, 785-830

Abstract: Abstract We consider the Volterra integro-differential equation with a time-dependent prox-regular constraint that changes in an absolutely continuous way in time (a Volterra absolutely continuous time-dependent sweeping process). The aim of our paper is twofold. The first one is to show the solvability of the initial value problem by setting up an appropriate catching-up algorithm (full discretization). This part is a continuation of our paper (Bouach et al. in arXiv: 2102.11987. 2021) where we used a semi-discretization method. Obviously, strong solutions and convergence of full discretization scheme are desirable properties, especially for numerical simulations. Applications to non-regular electrical circuits are provided. The second aim is to establish the existence of optimal solution to an optimal control problem involving the Volterra integro-differential sweeping process.

Keywords: Variational analysis; Moreau’s sweeping process; Moreau’s catching-up algorithm; Volterra integro-differential equation; Differential inclusions; 49J40; 47J20; 47J22; 58E35; 74M15; 74M10; 74G25 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-021-01991-z

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